Naser, who heads the Bavarian network of banks known as Sparkassen, was chairman of the board of directors of BayernLB in 2007 when it bought the ailing real estate financier Hypo Group Alpe Adria (HGAA).
BayernLB, which is owned by the Bavarian government, was force to sell its majority share in HGAA earlier this month to the Austrian government for a nominal price of €1, costing the state an estimated €3.75 billion.
Austria had insisted on nationalising the financier to safeguard the stability of its banking sector.
In his resignation statement, Naser, who is a former politician with the conservative Christian Social Union (CSU), took no responsibility for the HGAA purchase.
But observers widely applauded his decision to fall on his sword.
Bavarian Economy Minister Martin Zeil said: “I welcome it, if those who took the decisions at the time stand by their responsibility and take the necessary personal consequences.”
The opposition Social Democrats (SPD) and Greens described Naser's resignation as long overdue.
“It was high time that the man who stuck to his presidential perks like glue resigned,” said Eike Hallitzky, the Greens' parliamentary spokesman for finance.
The vice chairman of the Bavarian parliamentary committee that oversees BayernLB, Inge Aures, said that, because Naser had shaped the direction of BayernLB for many years, he was also responsible for another debacle, the loss of billions through asset-backed securities on the US mortgage market.
“Nasser wanted to spin the whole great wheel and he's catastrophically come to grief.”
Aures, an SPD member of the state parliament, called for the resignations of other former BayernLB directors.
“I'm also waiting for the CSU parliamentary leader in Bavaria, Georg Schmid; the chairman of the business committee in the Bavarian parliament and former CSU chairman Erwin Huber; the former Premier Günther Beckstein and also the Dachau district administrator Hansjörg Christmann to finally accept the consequences.”
They had all approved the 2007 purchase, he said.
Economy Minister Zeil also said: “The exposure of the BayernLB to the Hypo Group Alpe Adria was in hindsight a fatally flawed decision. It has cost the Bavarian taxpayer €3.75 billion. This disaster must be fully explained.”
The Greens' Hallitzky also criticised the role played by the former Premier Edmund Stoiber, accusing him of “megalomania”.
Stoiber had loved the idea of BayernLB as a global player and had pushed actively for its expansion, he said.